Reddit mentions of Modular Forms and Fermat’s Last Theorem

> It would be like comparing wiles proof for FLT to an entire book about Modular Forms, Elliptic Curves and Galois Representations.

I have (mostly) read that book. It's nothing like Mochizuki's work.

The issue isn't that the theory has a bunch of definitions, most theories do. It's that the entire theory seems to be a bunch of definitions with no nontrivial work or minor applications, except one incredibly grand claim. It this is actually true, there would be nothing even remotely like that in the history of mathematics.

Edit:

> He has made an extremely terrible job communicating with the westerners yeah, but it does not seem to be the case for other japaneses as one of his colleagues wrote a 300 page summary on it

He's convinced a few people, maybe like 10-20, but that's not the same thing as convincing the entire japanese community. And the people he's convinced have also been incapable of explaining it to their colleagues (and not for lack of trying, it seems), which kind of makes it questionable whether they actually understand it, or just think they do. My understanding is that the 300 page summary didn't really help much.

What do you mean by the "Whole Proof"? How much do you want to assume? If you assume everything that is learned in a standard phd program that is loosely related to number theory (so including things like Class Field Theory, basic theory of Elliptic curves and Modular forms), you would need the Langlands-Tunnell Theorem, which is a whole book on its own, Ribet's Theorem and the analysis of Frey Curves, Deformation Theory, Hecke Algebras, a boatload of advanced Commutative Algebra and many computational results on particular elliptic/modular curves. Then you can begin to talk about Wiles' contributions. It wouldn't be just one book.

If you want something that contains the general knowledge of the proof, but is brief when it needs to be, then Modular Forms and Fermat's Last Theorem is pretty solid.

This book supposedly covers the proof and much of the background material: Modular Forms and Fermat's Last Theorem (Springer). Of course, you'll probably have to consult many, many other books along the way, but this looks good as a point of reference.

Ah yes, if you ever get stuck there's a lovely book to consult along the way!